You’re leaving out the fact that Miller, a heavy underdog, actually beat the incumbent Murkowski in the Republican primary. I think Palin was largely responsible for that. What happened after that was that Miller ran a horrible campaign and committed political suicide when he tried , for whatever reason to distance himself from Palin.
I would expect Palin’s candidate to beat Murkowski in a GOP primary. We are talking about statewide, and her guy lost to a write-in.